## 1. Introduction

[2] Over the last decade, remarkable progress has been made in the development of communication systems. Among them, noise figure, gain, output power, and efficiency at millimeter-wave frequencies have been improved significantly. However, the demand of wireless broadband communication at millimeter-wave frequency recently increased rapidly due to activities of digital multimedia-contents circulation. One of the most important problems of millimeter-wave communication is the large transmission loss in free space. For instance, the transmission loss of a signal at 60 GHz frequency for 5 meters distance between transmitter and receiver is about 82 dB [*Shiomi and Yamamoto*, 2002]. Therefore antennas with high output radiation power are required to compensate for the large transmission loss.

[3] Parallel-plate waveguide (PPW) with a flange surface is known as a fundamental structure widely used for electromagnetic wave radiation (as, e.g., feed horns, flush-mounted antennas). Although exact closed-form solutions are available only in few cases, the waveguide radiation behavior has been well understood using a number of numerical techniques and approximate theories [*Rudduck and Wu*, 1969; *Wu et al.*, 1969; *Lee*, 1970; *Hongo*, 1972; *Itoh and Mittra*, 1974; *Hongo et al.*, 1975; *Lee and Grun*, 1982; *Leong et al.*, 1988; *Butler et al.*, 1991; *Kim et al.*, 1993; *Park and Eom*, 1993; *Lee et al.*, 1996]. However, since most of the studies were based on approximate solutions, the presented results have been restricted to the problem of perpendicularly flanged PPW. Moreover, all the previous considerations were based upon the basic assumptions of infinite flange surface, which is not infinite in practice. It is therefore desirable to discuss the radiation properties of a PPW with an arbitrarily flanged surface of finite size, which is expected to enhance the output radiation power. Unfortunately, before this paper we could not find a method that can solve this problem accurately.

[4] Accordingly, in this paper the radiation properties of a PPW with an arbitrarily flanged surface of finite size are carried out by using the BEM based on the GMEIEs. The GMEIEs used here are derived for the problem of a dielectric-filled PPW with a tilted flange surface of finite size, as shown in Figure 1a, but it is possible to apply them to other problems, for example, a dielectric-filled PPW with a tapered flange surface of finite size, as shown in Figure 1b.

[5] The numerical results of computer simulations are presented. The reflection coefficient, the reflected and radiated powers as well as the radiation pattern are calculated numerically for an incident TM_{0} (i.e., TEM) guided-mode wave. The results are compared with those reported in the literature, and are confirmed by the law of energy conservation.